TRACT 36.

THE WHIRLING-MACHINE.

193

the cone to its path or axis. So that, in this instance, the re-sistance is directly as the sine of the angle of incidence, thetransverse section beins the same.

(7). Hence may be determined what will be the altitudeof a column of air, whose pressure shall he equal to the re-sistance of a body, moving through it with any velocity. Thus,Let a = the area of the section of the body, similar to anyof those in the table, perpendicular to the direc-tion of motion ;

r = the resistance to the velocity in the table ; andx = the altitude sought, of a column of air, whosebase is a , and its pressure r.

Then ax = the content of the column in feet,and 1 ^ax or |ax its weight in ounces;

therefore |ax = r, and x — ■§• x ~ a is the altitude sought infeet, namely, of the quotient of the resistance of any bodydivided by its transverse section ; which is a constant quan-tity for all similar bodies, however different in magnitude,since the resistance r is nearly as the section a, as was foundin art. 1. When a — •§• of a foot, as in all the figures inthe foregoing table, except the small hemisphere: then,x = £ x —, becomes x = \ b r, where r is the resistance inthe table, to the similar body.

If, for example, we take the convex side of the large he-misphere, whose resistance is *634 oz to a velocity of 16 feetper second, then r = *634, and x = — 2‘3775 feet, is the

altitude of the column of air whose pressure is equal to theresistance on a spherical surface, with a velocity of 16 feet.And to compare the above altitude with that which is due tothe given velocity, it will be 32 3 : 16 1 : : 16 : 4, the altitudedue to the velocity 16; which is near double the altitudethat is equal to the pressure. And as the altitude is propor-tional to the square of the velocity, therefore, in small velo-cities, the resistance to any spherical surface, is equal to thepressure of a column of air on its great circle, whose altitudeis -ff or -594 of the altitude due to its velocity.

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